How to shift layers 4 layers ahead
I don't know of any add-on that specifically has a bump up by n layers feature, Blender has a massive eco-system for add-ons. Sometimes it's  easier to write a small script than to go looking for an add-on.

Here a small script that moves all items that appear in layers {5,6,7,8,9} up by 5 layers to {10,11,12,13,14} respectively. (I think you accidentally gave an example that is off by one)



You may want to test how this works in a small dummy .blend file, so you are confident using it in a production scenario.

paste this directly into the TextEditor and press Run.

import bpy

for obj in bpy.data.objects:

    # let's deal with a simple case: is it only on one layer?
    if obj.layers[:].count(True) == 1:
        found_index = obj.layers[:].index(True)
        if (5 &lt;= found_index &lt;= 9):
            new_index = found_index + 5
            obj.layers[:] = [i==new_index for i in range(20)]